Suppose you have a 50.0g sample of ice at -30.0 C. How many joules of heat energy are needed to heat the ice to 0.0 C? How many joules of heat energy are needed to melt the ice? I do not know how to set either of these up.
50 g sample of ice.
-30 C initial T
0 C final T
q = mass ice x specific heat solid ice x (Tfinal-Tinitial) = ?
To melt the ice at zero to water at zero.
q = mass ice x heat fusion ice = ?
To find the heat energy needed to heat the ice from -30.0°C to 0.0°C, we can use the specific heat capacity of ice and the formula:
Q = m * c * ΔT
where:
Q is the heat energy in joules,
m is the mass of the ice in grams,
c is the specific heat capacity of ice, and
ΔT is the change in temperature.
1. Calculating the heat energy to raise the temperature from -30.0°C to 0.0°C:
The specific heat capacity of ice is 2.09 J/g°C. We have a mass of 50.0 g, and the change in temperature is from -30.0°C to 0.0°C.
Q = 50.0 g * 2.09 J/g°C * (0.0°C - (-30.0°C))
Q = 50.0 g * 2.09 J/g°C * 30.0°C
Calculating this will give us the amount of heat energy needed to raise the temperature.
2. Calculating the heat energy needed to melt the ice:
To melt the ice, we need to convert it from a solid to a liquid without changing its temperature. The heat energy required for this phase change is given by:
Q = m * ΔH_fusion
where:
Q is the heat energy in joules,
m is the mass of the ice in grams, and
ΔH_fusion is the heat of fusion.
The heat of fusion for ice is 334 J/g.
Now we can plug in the values:
Q = 50.0 g * 334 J/g
Calculating this will give us the amount of heat energy needed to melt the ice.
Remember to use the correct sign conventions in the calculations. Heat energy being absorbed by the system is positive, while heat energy being released by the system is negative.